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I_laff
I've seen the derivation for the adiabatic expansion of an ideal gas which gives the result ## TV^{\gamma - 1} = constant ## which I understand. I have also seen the a similar result, ## pV^{\gamma} = constant ##. But I can't see how to get from the first expression to the second. Any ideas?

Gold Member
If you put ##\frac{PV}{nR}## in place of ##T## in the first equation, doesn't it become the second one, assuming that the number of moles ##n## remains constant in the expansion?

I_laff
From doing that you get ## pV^{\gamma} = R(constant) ##. So you just define a new constant on the RHS that contains ## R ##?

Gold Member
Isn't this a straightforward bit of Text Book derivation? Do you not have access to one?

Gold Member
Yes, it's a different constant then, the original one multiplied by ##nR##.

Gold Member
If you don't have a textbook, try the Hyperphysics website. They have a fair amount of stuff on the gas laws.

I_laff
I_laff
Isn't this a straightforward bit of Text Book derivation? Do you not have access to one?
You are probably right, however I don't have a textbook on thermodynamics. I thought of substituting ## \frac{pV}{nR} ## but didn't see how to remove ## nR ## from the final expression. Since they're constant, I guess it's obvious the new constant contains these terms.

I_laff
If you don't have a textbook, try the Hyperphysics website. They have a fair amount of stuff on the gas laws.
Thanks, I'll check it out .